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pottersheep
 3 years ago
Grade 12 math help please!! For what value of b will the polynomial p(x) = 2x^3 + bx^2  5x +2 have the same remainder when it is divided by x  2 and x+1?
pottersheep
 3 years ago
Grade 12 math help please!! For what value of b will the polynomial p(x) = 2x^3 + bx^2  5x +2 have the same remainder when it is divided by x  2 and x+1?

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TAKEBACKMATH
 3 years ago
Best ResponseYou've already chosen the best response.0okay I will show you:

TAKEBACKMATH
 3 years ago
Best ResponseYou've already chosen the best response.0sorry, it too late for me I will hand this over to lonesome else?

Callisto
 3 years ago
Best ResponseYou've already chosen the best response.1Here it goes~ Have you learnt remainder theorem yet?

Callisto
 3 years ago
Best ResponseYou've already chosen the best response.1@pottersheep Are you there??

pottersheep
 3 years ago
Best ResponseYou've already chosen the best response.1Yes sorry, we have!

Callisto
 3 years ago
Best ResponseYou've already chosen the best response.1So, let R be the remainder when p(x) is divided by x2. By remainder theorem, what would you get? I mean p(_) = ...?

pottersheep
 3 years ago
Best ResponseYou've already chosen the best response.1So i'd sub in 2 for x

pottersheep
 3 years ago
Best ResponseYou've already chosen the best response.1Sorry what do I do with the b though?

Callisto
 3 years ago
Best ResponseYou've already chosen the best response.1Right, so for p(2), you get p(2) = 4b  24 = R, agree? (By remainder theorem, p(a) = R , when p(x) is divided by xa)

Callisto
 3 years ago
Best ResponseYou've already chosen the best response.1And what is the remainder when p(x) is divided by x+1 ?

Callisto
 3 years ago
Best ResponseYou've already chosen the best response.1Not really.. Remainder = p(1) = 2(1)^3 + b(1)^2  5(1) +2 = ...?

pottersheep
 3 years ago
Best ResponseYou've already chosen the best response.1Opps, sorry! I subbed in 1!

Callisto
 3 years ago
Best ResponseYou've already chosen the best response.1Yes. Note that the remainder is p(x) = R when p(x) is divided by xa. Now, p(x) is divided by x+1, so a = 1 in the case. [ x(1) = x+1]

Callisto
 3 years ago
Best ResponseYou've already chosen the best response.1From the question, the polynomial p(x) = 2x^3 + bx^2  5x +2 have the same remainder when it is divided by x  2 and x+1. So, equate the two remainder you got and solve b. Got it?

pottersheep
 3 years ago
Best ResponseYou've already chosen the best response.1Ohhhhhhhhh, so make them equal to each other?? Yes I get it, thank you!!!!!!

Callisto
 3 years ago
Best ResponseYou've already chosen the best response.1Yes. Since they have the SAME remainder! You're welcome :)
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